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arXiv · 2611.01024

On the classification of entire solutions to the Allen-Cahn equation in any dimension

Alberto Farina
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Abstract

The mathematical content that follows dates from 9 March 2016. I began writing it in early December 2014, whilst I was visiting Scuola Normale Superiore in Pisa, Italy. I would like to thank Luigi Ambrosio, Andrea Malchiodi, Carlo Mantegazza e Gérard Tronel who, between January 2015 and March 2016, read this version of the manuscript and some earlier drafts. Their feedback and constant support have been a source of encouragement. The manuscript has been at rest since March 2016. Neither its content nor its status will undergo changes in the future; it asks merely to be considered through the eyes of that moment. Paris, October 23, 2026, Alberto Farina

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Alberto Farina. 2026-10-31. On the classification of entire solutions to the Allen-Cahn equation in any dimension. https://arxiv.org/abs/2611.01024

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